Re: [SI-LIST] : RE: Split Plane

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From: Doug McKean (dmckean@corp.auspex.com)
Date: Thu May 25 2000 - 16:49:10 PDT


Woops ...

Didn't mean to start anything.

The following derivation uses the -3dB point
or critical frequency for a passive circuit.

- Doug McKean

--------------------------------------------------

Assume V(0) = 0 and V(infinity) = Vmax

Look at only V = 10%Vmax and V = 90%Vmax

Since, V = Vmax*[1 - exp(-t/tau)]

(tau being whatever time constant you wish)

----------
V at 10% ...

  V(0.1) = 0.1*Vmax = Vmax - Vmax*exp(-t/tau)

  Vmax*exp(-t/tau) = Vmax - 0.1*Vmax
                   = 0.9*Vmax

  exp(-t/tau) = 0.9
  ln[exp(-t/tau)] = ln[0.9]
  (-t/tau) = -.1
  t(10%) = 0.1*tau

----------
V at 90% ...

  V(0.9) = 0.9*Vmax = Vmax - Vmax*exp(-t/tau)

  Vmax*exp(-t/tau) = Vmax - 0.9*Vmax
                   = 0.1*Vmax

  exp(-t/tau) = 0.1
  ln[exp(-t/tau)] = ln[0.1]
  (-t/tau) = -2.3
  t(90%) = 2.3*tau

----------
Trise = t(90%) - t(10%)
      = 2.3*tau - 0.1*tau
      = 2.2*tau

Since, f = 1/(2*pi*tau)

       makes tau = 1/(2*pi*f)

       Trise = 2.2*tau
             = 2.2/(2*pi*f)
             = 0.35014/f

       f = 0.35014/Trise

----------

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